If A \ B = A ∩ C and A ∩ B = A \ C, what is A ∩ B ∩ C?
Answer and explanation
Correct answer: ∅
From A ∩ B = A \ C, every element of A ∩ B belongs to A but does not belong to C. Hence no element can simultaneously belong to A ∩ B and C. Since A ∩ B ∩ C consists precisely of elements common to A, B, and C, it follows that A ∩ B ∩ C = ∅. The first given equality is consistent with this result but is not needed for the final conclusion.
Frequently asked questions
What is the correct answer to this question?
∅
Why is this the correct answer?
From A ∩ B = A \ C, every element of A ∩ B belongs to A but does not belong to C. Hence no element can simultaneously belong to A ∩ B and C. Since A ∩ B ∩ C consists precisely of elements common to A, B, and C, it follows that A ∩ B ∩ C = ∅. The first given equality is consistent with this result but is not needed for the final conclusion.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
